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In this paper, we introduce and solve the following additive s-functional inequality 8.1 \(\begin{aligned} \left\| f\left( x+y\right) +f(x-y)- 2f(x )\right\| \le \Vert s (f(x+y)-f(x)-f(y))\Vert , \end{aligned}\) where s is a fixed nonzero complex number with \(|s|<1\) . Using the fixed point method and the direct method, we prove the Hyers–Ulam stability of the additive s-functional inequality (8.1) in complex Banach spaces. Furthermore, we introduce hom-derivations in Lie Banach algebras and prove the Hyers–Ulam stability of hom-derivations in complex Lie Banach algebras.

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Hom-Derivations in Lie Banach Algebras

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  • 发表日期：

    2026年

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  • Siriluk Donganont,
  • Choonkil Park,
  • Michael Th. Rassias

摘要

In this paper, we introduce and solve the following additive s-functional inequality 8.1 \(\begin{aligned} \left\| f\left( x+y\right) +f(x-y)- 2f(x )\right\| \le \Vert s (f(x+y)-f(x)-f(y))\Vert , \end{aligned}\) where s is a fixed nonzero complex number with \(|s|<1\) . Using the fixed point method and the direct method, we prove the Hyers–Ulam stability of the additive s-functional inequality (8.1) in complex Banach spaces. Furthermore, we introduce hom-derivations in Lie Banach algebras and prove the Hyers–Ulam stability of hom-derivations in complex Lie Banach algebras.